Problem: Simplify the following expression: $ q = \dfrac{a - 7}{10a} - \dfrac{5}{7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{a - 7}{10a} \times \dfrac{7}{7} = \dfrac{7a - 49}{70a} $ Multiply the second expression by $\dfrac{10a}{10a}$ $ \dfrac{5}{7} \times \dfrac{10a}{10a} = \dfrac{50a}{70a} $ Therefore $ q = \dfrac{7a - 49}{70a} - \dfrac{50a}{70a} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{7a - 49 - 50a }{70a} $ Distribute the negative sign: $q = \dfrac{7a - 49 - 50a}{70a}$ $q = \dfrac{-43a - 49}{70a}$